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How to Find the Area of a Box When You Know the Volume

Knowing the volume of a box that has equal sides, which is a cube, allows you to find the box's surface area. If a box does not have equal sides, then you cannot use its volume to find its surface area. The equation of a cube's volume is: volume = length x width x height. When all sides of a box are equal, you may cube one side's measurement to find volume; the equation is: 2 cubed = 2 x 2 x 2 = 8. Therefore, the cube root of the box's volume is the measurement for one side of the box. Once you have one side's measurement, designated as "a," you can apply the formula for surface area: 6 x a squared.

Things You'll Need

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Instructions

    • 1

      Reverse the volume formula, which is length x width x height = volume, to find the cube root of the box's volume, 3√volume. If your calculator does not have a cube root function, 3√ , then determine the number that divides into the volume three times.

      If the volume is 8, for example, then the cube root equation is: 3√8 = 2 Because 2 divides into 8 three times (2 x 2 x 2 = 8), the cube root of 8 is 2.

    • 2

      Apply the surface area formula, 6 x "a" squared. In the formula, "a" is the side measurement of your box. Square "a" first. Squaring a number means to multiply it by itself.

      If a = 2, for example, then square 2; 2 squared = 2 x 2 = 4. The result is the area of one side of the box.

    • 3

      Multiply "a" squared by all six sides of the box to find the box's total surface area. For example, the equation to find the surface area of a box with a volume of 8 cubic is 6 x 4 = 24.

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